Celtic is as much a meaningful musical term as World Music.

Many people here in England who are not into folk music think that all folk music is, by definition, Irish. The Irish are Celts. Therefore all folk music is Celtic.

To my ears, the main difference I hear between Irish music and English music is in the playing styles. In the Irish music I hear in England the playing is, usually, technically very good but, to my mind, the main aim of the musicians seem to be speed and ornamentation. Whereas the English tunes generally seem to be played at slower speeds with a much more rythmic feel. I think you can dance more easily to most English tunes than you can Irish.

For some English style dance bands (English Ceilidh) look up:
The Old Swan Band
Burlsdon Village Band
Hekety
Random
Tickled Pink
Peeping Tom
The Committee Band
The Bismarcks
Mawkin
The Gloworms
Florida
All Blacked Up
Dartmoor Pixie Band
Many of these bands play tunes of Irish origin and it's interesting to compare their versions with those from the 'Celtic' versions.

My own hugely sweeping statement with too many exceptions to the rule is that "The Irish style is candy-floss as opposed to the English meat and two veg".

For Singing there are two excellent CDs from Fellside: Voices and Voices in Harmony. Another recommendation for Spiers and Boden, Bellowhead, any Carthies and Kathryn Tickell. But also: Witches of Elswick, Jane and Amanda Threllfall; Crucible.